<This journal of mine got the highest grade in our Math Subject. Hope that my work helps other educators too! >
December 13, 2011, Tuesday at 6:09 in the late afternoon, I am reading my journal in Geometry. I do not have choice but to do it because it is our duty- a duty for us to accomplish this requirement. The deadline of submission is on December 16, 2011, Friday. I only have three more days to complete my reaction paper. I hope I can finish it before that day comes. I hope I have the ideas to fill up the empty space in the bond paper. I hope I have an open mind to understand what I will be reading. Oh gosh! My time starts at 1, 2… 3!
I figure out doing that intro so that Ma’am can know that I am really reading my journal. Ha-ha! Another reason is for me to react immediately on what I have read. It is because my thoughts are fading easily. That is why I have to write at once. If I do not respond to this, I will have hard time thinking on what I will put on this paper. Well, anyways, let us proceed with my reflection.
“… children were more successful with manipulative than with pictures …, all children were more likely to rotate their paper or physical shape when this action could help them identify the shape.” These are some lines that can be found in my journal. While I was reading these, I remembered Prof. Pabayos, exclusively during the time she is teaching the prisms. As she draws the geometric figure, specifically the cube-figure, I and my classmates are thoroughly watching. When she is done, we try to stop ourselves from laughing at her drawing. I won’t describe anymore what the image looks like. But what makes it more funny is when she told us, “Isipin niyo na lang na cube ‘yan. [Smile].” After that, one of my classmates volunteered to improve the drawing. Suddenly, our professor told us, “Hindi talaga ako marunong mag-drawing.” And then, we laughed again.
I did not include that just to make fun of our professor. I would simply like to address the issue that not all teachers in Mathematics, particularly in Geometry, are good in illustrating a certain figure. There were some who cannot draw the object as good as how they want the image to appear. However, this doesn’t mean that they are not good in teaching their chosen field. It was just they don’t know how. So, to help them show to their students what their image truly looks, they have the visual shapes or manipulatives or the hands-on objects during the lesson. It is because students, especially elementary students, are more visual-oriented. They learn easily when they can see, touch, move or manipulate the objects by themselves.
“… manipulations still help children expand their investigations in the physical environment thereby advance their thinking.” This is the abstract formed by Taylor Martin, Ayiesha Lukong and Raven Reaves, faculties of the College of Education in The University of Texas at Austin, in their study entitled “The Roles of Manipulatives in Arithmetic and Geometry Tasks”. This study contains the effects of manipulatives not only in Geometry but also in Arithmetic. On the other hand, they did not forget to mention in their study that these manipulatives may have possible different effects in these two fields. They also noted that action with manipulatives supports learning when it provides a way for children to simultaneously and iteratively adapt and interpret their environment.
Many researchers and teachers and even I believe that these hands-on objects can help students learn mathematics concepts. For example, when the topic of the day is about fraction, the teacher would prepare fraction pies. These are broken pieces shaped like a piece of pizza taken from the whole. The teacher will use this to illustrate the concepts found in fractions. Thus, help him or her in teaching the students the fraction operations and meanings in the easy way.
I was once a student who learned fractions from my first year professor with the help of these fraction pies or as what they call it manipulatives. I am a student who really has a bad background in understanding fraction operations. Honestly, I always got low grades when fractions are the topic of the day. That is why I am easily irritated and don’t even have the patience to listen and participate during class discussions. But during my first semester in my first year college, my views about fractions change. Through these manipulatives, I am convinced to understand, somehow, the nature of fractions and learn to think of ways how I can solve fractional problems in my own ways. Up to now, that serves as my inspiration to think and use things that can help me teach my lessons to the students in the way that they can understand it easily. And so, I also believe what the researchers wrote about their study “On one hand, working with manipulatives improves ones’ performance on mathematical tasks in some cases.
According to the researchers, the best instructional strategy is to use multiple manipulatives to teach mathematical concepts. They do believe that exposure to multiple representations leads to better understanding of underlying mathematical principles. These manipulatives are viewed as external resources that primarily help problem solvers keep track of the problem elements without wasting internal memory resources. Based on how I understand these lines, this strategy can help the students solve problems in distressful ways. Just take my example with the drawing of Prof. Pabayos. We might have a hard time solving geometrical problems such as finding the lateral and surface area and even the volume if she didn’t show us how the figure really looks like. Though we know the formula, it is still better to keep track on determining the personal location of the length, width and height in the certain prism. This is also to check if each one of us really knows how to locate especially personally the length and the width.
These manipulatives could be more helpful in geometry because they are more similar to the objects operated on and resembles the outcomes of problem solving. Another thing, in geometry, physical shapes and children concepts of shapes may nearly identical, particularly in early stages of learning. Lastly, working with the virtual manipulatives helped children develop conceptual and procedural knowledge in geometry, and that virtual manipulatives are more motivating than paper and pencil tasks.